On an algebraicity theorem of Kontsevich

Abstract

We give in a particular case a combinatorial proof of a recent algebraicity result of Kontsevich; the proof uses generalized one-sided and two-sided Dyck words, or equivalently, excursions and bridges. We indicate a noncommutative version of these notions, which could lead to a full proof. We show also a relation with pointed planar maps.

Keywords

• algebraic series
• dyck words
• noncommutative
• planar maps.
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]